This review discusses Operator Inference, a nonintrusive reduced modeling approach that
incorporates physical governing equations by defining a structured polynomial form for the …

This paper accompanies FOSSIL: a software tool for the synthesis of Lyapunov functions
and of barrier certificates (or functions) for dynamical systems modelled as differential …

This paper presents an approach of safety verification based on neural networks for
continuous dynamical systems which are modeled as a system of ordinary differential …

We introduce an automated, formal, counterexample-based approach to synthesise Barrier
Certificates (BC) for the safety verification of continuous and hybrid dynamical models. The …

Model-based reinforcement learning has been widely studied for controller synthesis in
cyber-physical systems (CPSs). In particular, for safety-critical CPSs, it is important to …

A barrier certificate can separate the state space of a considered hybrid system (HS) into
safe and unsafe parts according to the safety property to be verified. Therefore this notion …

This article proves the completeness of an axiomatization for differential equation invariants
described by Noetherian functions. First, the differential equation axioms of differential …

Barrier certificates provide safety guarantees for hybrid systems. In this paper, we propose a
novel approach to synthesizing neural networks as barrier certificates. Candidate networks …

The reachability problem is one of the most important issues in the verification of hybrid
systems. But unfortunately the reachable sets for most of hybrid systems are not computable …

Safety verification is an essential requirement of neural network controlled systems when
they are adopted in safety-critical fields. This paper proposes a novel approach to …